A New Method of Numerical Differential and Time Domain Integral Based on the Analysis of Vibration Response

Abstract

A new method of numerical differentiation and time domain integral was proposed in this paper, its idea was originated from the analysis of the time domain vibration response. As to numerical differentiation, the discrete sequence could be considered as the displacement response of an one degree-of-freedom system, and the velocity and acceleration response corresponding to the first and second order numerical differentiation. As to time domain integral, the discrete sequence could be considered as the acceleration response of an one degree-of-freedom system, and the velocity and displacement response corresponding to the first and second order time domain integral. All these work were established based on the discretization analysis of Duhamel integral. Numerical simulation result indicates the effective and better accuracy of this new method.